Mandel, Jan; Tezaur, Radek Convergence of a substructuring method with Lagrange multipliers. (English) Zbl 0880.65087 Numer. Math. 73, No. 4, 473-487 (1996). The convergence of a substructuring iterative method with Lagrange multipliers is analyzed. This method was recently proposed by C. Farhat and F.-X. Roux [Int. J. Numer. Methods Eng. 32, No. 6, 1205-1227 (1991; Zbl 0758.65075)]. The method decomposes finite element discretization of an elliptic boundary value problem into Neumann problems on the subdomains plus a coarse problem for the subdomain nullspace components. For linear conforming elements and preconditioning by the Dirichlet problems on the subdomains, an asymptotic bound on the condition number is derived. Reviewer: W.Heinrichs (Essen) Cited in 3 ReviewsCited in 53 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 65F35 Numerical computation of matrix norms, conditioning, scaling Keywords:Lagrange multipliers; substructuring iterative method; convergence; finite element; preconditioning; condition number Citations:Zbl 0758.65075 PDFBibTeX XMLCite \textit{J. Mandel} and \textit{R. Tezaur}, Numer. Math. 73, No. 4, 473--487 (1996; Zbl 0880.65087) Full Text: DOI